1.
A room is in the shape of a cuboid. Its floor measures 7.2 m by 9.6 m and its height is 3.5 m.
(a)
Calculate the length of AC.
(b)
Calculate the length of AG.
(c)
Calculate the angle that AG makes with the floor.
(a)
AC2 = 7.22 + 9.62
AC = 12 m
(b)
AG2 = 122 + 3.52
AG = 12.5m
(c)
tan θ =
3.5
3.5
12
or sin θ =
or cos θ =
12
12.5
12.5
θ = 16.3°
2.
In the diagram, AD = 4 m, AB = 9 m, BC = 10 m, BD̂A = 90° and DB̂C = 100°.
(a)
Calculate the size of AB̂C .
(b)
Calculate the length of AC.
(a)
sin AB̂D 
(b)
AC2 = 102 + 92 – 2 × 10 × 9 × cos(126.38...)
4
9
100 + their (AB̂D)
126°
AC = 17.0 m
3.
Pauline owns a piece of land ABCD in the shape of a quadrilateral. The length of BC is 190
m, the length of CD is 120 m, the length of AD is 70 m, the size of angle BCD is 75° and the
size of angle BAD is 115°.
Pauline decides to sell the triangular portion of land ABD. She first builds a straight fence
from B to D.
(a)
Calculate the length of the fence.
The fence costs 17 USD per metre to build.
(b)
Calculate the cost of building the fence. Give your answer correct to the nearest USD.
(c)
Calculate the size of angle ABD, correct to three significant figures.
(d)
Calculate the area of triangle ABD.
(a)
BD2 = 1902 + 1202 –2(190)(120)cos75°
= 197 m
(b)
cost = 196.717... × 17
= 3344 USD
Note: Accept 3349 from 197.
(c)
sin( ABD) sin(115)

70
196.7
= 18.81°...
= 18.8°
(d)
angle BDA = 46.2°
70  (196 .717...)  sin( 46.2)
Area =
2
Area of ABD = 4970 m2
4. The diagram shows triangle ABC in which angle BÂC = 30°, BC = 6.7 cm and AC = 13.4 cm.
(a)
Calculate the size of angle AĈB .
Nadia makes an accurate drawing of triangle ABC. She measures angle BÂC and finds it to
be 29°.
(b)
(a)
Calculate the percentage error in Nadia’s measurement of angle BÂC
sin AB̂C sin 30

13.4
6 .7
.
AB̂C = 90°
AĈB = 60°
(b)
29  30
× 100
30
% error = –3.33 %